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Infinity and Beyond

s-anthony
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8/21/2012 1:17:30 PM
Posted: 4 years ago
Can you measure an infinite line? If so, who decides what an inch of that line is? Can you say I traveled one mile along an infinite pathway or spent one hour of eternity? If you had an endless amount of money, could you say one tenth has been spent?

The question remains, what are you measuring against, an inch, a mile, an hour, or a tenth of what? Measurements are merely meant to quantify an object, and quantification demands a set amount. For instance, an inch is one-tweflth of a foot, and a foot is one-third of a yard, a yard is merely three feet of a mile, and a mile etc.... With infinity we would go on forever, never reaching its greatest length. In fact, it has no end. It cannot be defined, by any sort of measurement. This same idea not only applies to the line but any thing you choose to modify.
caveat
Posts: 2,137
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8/21/2012 1:22:41 PM
Posted: 4 years ago
At 8/21/2012 1:17:30 PM, s-anthony wrote:
Can you measure an infinite line?
No.
If so, who decides what an inch of that line is?
Yes.
Can you say I traveled one mile along an infinite pathway
Yes.
or spent one hour of eternity?
Yes.
If you had an endless amount of money, could you say one tenth has been spent?
No.

Perhaps you should make sure your examples are relevant to your point before posting. Inches, miles, and hours are arbitrarily, objectively, and wholly defined by humans. An inch of an infinitely long string and an inch of a two-inch long string are both still an inch. A tenth of an infinitely long string, however, is another matter.

The question remains, what are you measuring against, an inch, a mile, an hour, or a tenth of what? Measurements are merely meant to quantify an object, and quantification demands a set amount. For instance, an inch is one-tweflth of a foot, and a foot is one-third of a yard, a yard is merely three feet of a mile, and a mile etc.... With infinity we would go on forever, never reaching its greatest length. In fact, it has no end. It cannot be defined, by any sort of measurement. This same idea not only applies to the line but any thing you choose to modify.

Ok.
There is an art, it says, or rather, a knack to flying. The knack lies in learning how to throw yourself at the ground and miss. " Clearly, it is this second part, the missing, which presents the difficulties.
caveat
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8/21/2012 1:23:28 PM
Posted: 4 years ago
At 8/21/2012 1:22:41 PM, caveat wrote:
If so, who decides what an inch of that line is?
Actually, I suppose I can't answer this question since my answer to its precursor was no.
There is an art, it says, or rather, a knack to flying. The knack lies in learning how to throw yourself at the ground and miss. " Clearly, it is this second part, the missing, which presents the difficulties.
bossyburrito
Posts: 14,075
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8/21/2012 1:40:00 PM
Posted: 4 years ago
No. Infinity is infinite.
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
tBoonePickens
Posts: 3,266
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8/21/2012 4:21:05 PM
Posted: 4 years ago
At 8/21/2012 1:17:30 PM, s-anthony wrote:
Can you measure an infinite line?
No.

If so, who decides what an inch of that line is?
Can't, it is meaningless.

Can you say I traveled one mile along an infinite pathway or spent one hour of eternity?
No because 0, 1, 2, and any other value other than infinity would be indistinguishable from each other. In essence there would be only 2 things: infinity and not infinity.

If you had an endless amount of money, could you say one tenth has been spent?
No.

The question remains, what are you measuring against, an inch, a mile, an hour, or a tenth of what?
You are measuring a portion of the whole.

Measurements are merely meant to quantify an object, and quantification demands a set amount. For instance, an inch is one-tweflth of a foot, and a foot is one-third of a yard, a yard is merely three feet of a mile, and a mile etc....
And of course it becomes circular at some point down the line.

With infinity we would go on forever, never reaching its greatest length. In fact, it has no end. It cannot be defined, by any sort of measurement. This same idea not only applies to the line but any thing you choose to modify.
Bingo! It cannot be defined recursively AND be complete. That is why infinity is the whole; not a never ending whole but simply the whole -and the rest are subdivisions of said whole.
WOS
: At 10/3/2012 4:28:52 AM, Wallstreetatheist wrote:
: Without nothing existing, you couldn't have something.
The_Fool_on_the_hill
Posts: 6,071
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8/21/2012 7:03:45 PM
Posted: 4 years ago
At 8/21/2012 4:21:05 PM, tBoonePickens wrote:
At 8/21/2012 1:17:30 PM, s-anthony wrote:
Can you measure an infinite line?
No.

If so, who decides what an inch of that line is?
Can't, it is meaningless.

Can you say I traveled one mile along an infinite pathway or spent one hour of eternity?
No because 0, 1, 2, and any other value other than infinity would be indistinguishable from each other. In essence there would be only 2 things: infinity and not infinity.

If you had an endless amount of money, could you say one tenth has been spent?
No.

The question remains, what are you measuring against, an inch, a mile, an hour, or a tenth of what?
You are measuring a portion of the whole.

Measurements are merely meant to quantify an object, and quantification demands a set amount. For instance, an inch is one-tweflth of a foot, and a foot is one-third of a yard, a yard is merely three feet of a mile, and a mile etc....
And of course it becomes circular at some point down the line.

With infinity we would go on forever, never reaching its greatest length. In fact, it has no end. It cannot be defined, by any sort of measurement. This same idea not only applies to the line but any thing you choose to modify.
Bingo! It cannot be defined recursively AND be complete. That is why infinity is the whole; not a never ending whole but simply the whole -and the rest are subdivisions of said whole.

The Fool: The fact that you have to define it rather then prove it suggest major problems. If it is all intergers is already a defintion. Why do you know need also definite it as infinite? I am pretty sure its false.
"The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another." G. W. F. HEGEL
Sidewalker
Posts: 3,713
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8/22/2012 6:30:41 AM
Posted: 4 years ago
At 8/21/2012 1:17:30 PM, s-anthony wrote:
Can you measure an infinite line? If so, who decides what an inch of that line is? Can you say I traveled one mile along an infinite pathway or spent one hour of eternity? If you had an endless amount of money, could you say one tenth has been spent?

No, but you are starting with basic mathematical concepts, and mathematics is a comnplete abstraction, and so is deductive logic. Fundamentl to the abstraction of mathematics, is the concept of numbers, applying values to the points on a line, another basic concept of mathematics, that is derived from applying basic mathematical operations, is that numbers are infinite.

The question remains, what are you measuring against, an inch, a mile, an hour, or a tenth of what? Measurements are merely meant to quantify an object, and quantification demands a set amount. For instance, an inch is one-tweflth of a foot, and a foot is one-third of a yard, a yard is merely three feet of a mile, and a mile etc.... With infinity we would go on forever, never reaching its greatest length. In fact, it has no end. It cannot be defined, by any sort of measurement. This same idea not only applies to the line but any thing you choose to modify.

You are equivocating here, mathematics is an abstraction, you are equivocating between abstract concepts and real measurements, this does nothing to reject the validity of mathematical concepts. It is sinply a matter of abstract thought.

You aren't talking about mathematics anymore if you reject abstract thought, and the basic concept of numbers.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
Sidewalker
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8/22/2012 6:31:48 AM
Posted: 4 years ago
At 8/21/2012 7:03:45 PM, The_Fool_on_the_hill wrote:
At 8/21/2012 4:21:05 PM, tBoonePickens wrote:
At 8/21/2012 1:17:30 PM, s-anthony wrote:

The Fool: The fact that you have to define it rather then prove it suggest major problems. If it is all intergers is already a defintion. Why do you know need also definite it as infinite? I am pretty sure its false.

I'm pretty sure you aren't grasping the basic concepts of abstract thought.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
The_Fool_on_the_hill
Posts: 6,071
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8/22/2012 5:51:22 PM
Posted: 4 years ago
At 8/22/2012 6:31:48 AM, Sidewalker wrote:
At 8/21/2012 7:03:45 PM, The_Fool_on_the_hill wrote:
At 8/21/2012 4:21:05 PM, tBoonePickens wrote:
At 8/21/2012 1:17:30 PM, s-anthony wrote:

The Fool: The fact that you have to define it rather then prove it suggest major problems. If it is all intergers is already a defintion. Why do you know need also definite it as infinite? I am pretty sure its false.

I'm pretty sure you aren't grasping the basic concepts of abstract thought.

The Fool: Well I know that I am note. And I have private access to my thoughts. VIA THE COGITO
"The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another." G. W. F. HEGEL
Sidewalker
Posts: 3,713
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8/22/2012 9:10:49 PM
Posted: 4 years ago
At 8/22/2012 5:51:22 PM, The_Fool_on_the_hill wrote:
At 8/22/2012 6:31:48 AM, Sidewalker wrote:
At 8/21/2012 7:03:45 PM, The_Fool_on_the_hill wrote:
At 8/21/2012 4:21:05 PM, tBoonePickens wrote:
At 8/21/2012 1:17:30 PM, s-anthony wrote:

The Fool: The fact that you have to define it rather then prove it suggest major problems. If it is all intergers is already a defintion. Why do you know need also definite it as infinite? I am pretty sure its false.

I'm pretty sure you aren't grasping the basic concepts of abstract thought.

The Fool: Well I know that I am note. And I have private access to my thoughts. VIA THE COGITO

Illogical thoughts =/= abstract thoughts.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
The_Fool_on_the_hill
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8/22/2012 9:15:08 PM
Posted: 4 years ago
At 8/22/2012 9:10:49 PM, Sidewalker wrote:
At 8/22/2012 5:51:22 PM, The_Fool_on_the_hill wrote:
At 8/22/2012 6:31:48 AM, Sidewalker wrote:
At 8/21/2012 7:03:45 PM, The_Fool_on_the_hill wrote:
At 8/21/2012 4:21:05 PM, tBoonePickens wrote:
At 8/21/2012 1:17:30 PM, s-anthony wrote:

The Fool: The fact that you have to define it rather then prove it suggest major problems. If it is all intergers is already a defintion. Why do you know need also definite it as infinite? I am pretty sure its false.

I'm pretty sure you aren't grasping the basic concepts of abstract thought.

The Fool: Well I know that I am not. And I have private access to my thoughts. VIA THE COGITO. That is you can't possibly know what I know. Therefore your claim is false by neccesity.

Illogical thoughts =/= abstract thoughts.

The Fool: What information here are you responding too?

Sidewalkers shamefull remarks so far:
- Illogical thoughts =/= abstract thoughts.

-I'm pretty sure you aren't grasping the basic concepts of abstract thought.
"The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another." G. W. F. HEGEL
s-anthony
Posts: 2,582
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8/22/2012 10:40:54 PM
Posted: 4 years ago
At 8/22/2012 6:30:41 AM, Sidewalker wrote:
No, but you are starting with basic mathematical concepts, and mathematics is a comnplete abstraction, and so is deductive logic. Fundamentl to the abstraction of mathematics, is the concept of numbers, applying values to the points on a line, another basic concept of mathematics, that is derived from applying basic mathematical operations, is that numbers are infinite.

Real and abstract are two sides to one coin. There is nothing you can call real that cannot, also, be used as an abstraction.
In fact, anything we experience, either directly or indirectly, is a composite of many different experiences projected into one time and space. We do not see with our eyes but with our brains; and, our brains are neurological complexes both inherited and stimulated by our environments. So, in a sense, everything is real, yet everything is abstract.

To say, that, numbers have the property of infinity is to take away any value or meaning they may have; for, an infinitely great number is a contradiction in terms; greatness is a comparative term, and infinity is comparative to nothing.
The_Fool_on_the_hill
Posts: 6,071
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8/22/2012 11:18:24 PM
Posted: 4 years ago
At 8/22/2012 10:40:54 PM, s-anthony wrote:
At 8/22/2012 6:30:41 AM, Sidewalker wrote:
No, but you are starting with basic mathematical concepts, and mathematics is a comnplete abstraction, and so is deductive logic. Fundamentl to the abstraction of mathematics, is the concept of numbers, applying values to the points on a line, another basic concept of mathematics, that is derived from applying basic mathematical operations, is that numbers are infinite.

Real and abstract are two sides to one coin. There is nothing you can call real that cannot, also, be used as an abstraction.
In fact, anything we experience, either directly or indirectly, is a composite of many different experiences projected into one time and space. We do not see with our eyes but with our brains; and, our brains are neurological complexes both inherited and stimulated by our environments. So, in a sense, everything is real, yet everything is abstract.

To say, that, numbers have the property of infinity is to take away any value or meaning they may have; for, an infinitely great number is a contradiction in terms; greatness is a comparative term, and infinity is comparative to nothing.

The Fool: Nice, I forgot about that argument.
"The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another." G. W. F. HEGEL
Sidewalker
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8/23/2012 6:04:05 AM
Posted: 4 years ago
At 8/22/2012 10:40:54 PM, s-anthony wrote:
At 8/22/2012 6:30:41 AM, Sidewalker wrote:
No, but you are starting with basic mathematical concepts, and mathematics is a complete abstraction, and so is deductive logic. Fundamental to the abstraction of mathematics, is the concept of numbers, applying values to the points on a line, another basic concept of mathematics, that is derived from applying basic mathematical operations, is that numbers are infinite.

Real and abstract are two sides to one coin. There is nothing you can call real that cannot, also, be used as an abstraction.

But there are abstractions that cannot be represented in reality. You can abstractly represent an infinite set, faster then light travel, time going in reverse, etc, often such abstractions are logically useful even though they cannot be observed in reality. The science of theoretical Cosmology abstractly runs time in reverse to arrive at rigidly deductive mathematical conclusions about the early universe. The fact that we cannot observe time running backward certainly doesn't mean such such abstract rational processes are meaningless or that they are not useful mathematically. Such abstractions are a very basic method of deductive and inductive logical thought processes in almost all sciences as well as everyday life. Think of how many basic math word problems you answered in grade school required such an abstract process of deductive logical thought (i.e. John traveled 50 miles an hour over a distance of 150 miles and arrived at 4:00 PM, when did he leave?) The answer was not some pseudo philosophical objection that you can't go backward in time so the question is meaningless.

I think the real problem here is that in some people the simple abstract mathematical concept of infinity conjures up an association with theological ideas and then hardened ideological agendas come into play, people get all bunged up and emotional, and the result is a bunch of pseudo philosophical nonsense. The abstract concept of mathematical infinity is not a particularly difficult concept and it only requires a straightforward logical process of applying first order logic quantifiers, it is very useful mathematically and logically, it is definitional regarding numbers, and it just isn't about God.

In fact, anything we experience, either directly or indirectly, is a composite of many different experiences projected into one time and space. We do not see with our eyes but with our brains; and, our brains are neurological complexes both inherited and stimulated by our environments. So, in a sense, everything is real, yet everything is abstract.

I would agree that what we refer to as the real world is the presumed cause of our sensations, but I don't think that means there is no difference between reality and abstraction, confusing the two is still a fallacy of equivocation.

To say, that, numbers have the property of infinity is to take away any value or meaning they may have; for, an infinitely great number is a contradiction in terms; greatness is a comparative term, and infinity is comparative to nothing.

I don't think mathematics says that numbers have the property of infinity, it says that the set of numbers has the property of infinity because you can abstractly apply a infinitely recurring mathematical operation to represent the set ( i.e. for every whole number N, there is a subsequent number represented by N+1). That does not make every number meaningless or equal to zero, each specific number still has a value that mathematical operations can apply to. The abstract concept of infinity is a basic axiom of mathematics and ZF set theory, and whether or not you can actually measure an infinite set in reality doesn't change the fact that the abstract concept exists mathematically.

Mathematics is an abstract science with axioms, definitions, and rules of first order logic, you can't simply deny the axioms, definitions, and rules and still be talking about mathematics.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
s-anthony
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8/23/2012 9:52:32 AM
Posted: 4 years ago
At 8/23/2012 6:04:05 AM, Sidewalker wrote:
But there are abstractions that cannot be represented in reality. You can abstractly represent an infinite set, faster then light travel, time going in reverse, etc, often such abstractions are logically useful even though they cannot be observed in reality. The science of theoretical Cosmology abstractly runs time in reverse to arrive at rigidly deductive mathematical conclusions about the early universe. The fact that we cannot observe time running backward certainly doesn't mean such such abstract rational processes are meaningless or that they are not useful mathematically. Such abstractions are a very basic method of deductive and inductive logical thought processes in almost all sciences as well as everyday life. Think of how many basic math word problems you answered in grade school required such an abstract process of deductive logical thought (i.e. John traveled 50 miles an hour over a distance of 150 miles and arrived at 4:00 PM, when did he leave?) The answer was not some pseudo philosophical objection that you can't go backward in time so the question is meaningless.

No. I would not say the question is meaningless, neither the answer. Both the question and the answer exist, in reality. In fact, everything you can conjure up has its place in reality. Only that which is real has existence, and only that which has existence can be known. I cannot know something that doesn't exist; for, if it doesn't exist, it is nothing. I know most people would disagree with me and say, "Santa Clause isn't real and, yet, he exists. " Yet, the question remains, where does he exist? He exists in the minds of good little boys and girls. So, in response, where does anything you have knowledge of exist? It exists in your mind.

Can you experience anything without using your mind? Does anything exist, apart from your knowledge of it? If it does, then, tell me what it is. You can't; because, you must be conscious of it.

By definition, the term infinity, whether saying an infinitely great universe or an infinitely great set of numbers, has no end ; so, for you, or anyone else, for that matter, to make the assumption that anything is infinite is, by mere reason, a logical fallacy.

I think the real problem here is that in some people the simple abstract mathematical concept of infinity conjures up an association with theological ideas and then hardened ideological agendas come into play, people get all bunged up and emotional, and the result is a bunch of pseudo philosophical nonsense. The abstract concept of mathematical infinity is not a particularly difficult concept and it only requires a straightforward logical process of applying first order logic quantifiers, it is very useful mathematically and logically, it is definitional regarding numbers, and it just isn't about God.

How can something that, by definition, cannot be defined, define anything?
Sidewalker
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8/23/2012 1:57:51 PM
Posted: 4 years ago
At 8/23/2012 9:52:32 AM, s-anthony wrote:
At 8/23/2012 6:04:05 AM, Sidewalker wrote:
But there are abstractions that cannot be represented in reality. You can abstractly represent an infinite set, faster then light travel, time going in reverse, etc, often such abstractions are logically useful even though they cannot be observed in reality. The science of theoretical Cosmology abstractly runs time in reverse to arrive at rigidly deductive mathematical conclusions about the early universe. The fact that we cannot observe time running backward certainly doesn't mean such such abstract rational processes are meaningless or that they are not useful mathematically. Such abstractions are a very basic method of deductive and inductive logical thought processes in almost all sciences as well as everyday life. Think of how many basic math word problems you answered in grade school required such an abstract process of deductive logical thought (i.e. John traveled 50 miles an hour over a distance of 150 miles and arrived at 4:00 PM, when did he leave?) The answer was not some pseudo philosophical objection that you can't go backward in time so the question is meaningless.

No. I would not say the question is meaningless, neither the answer. Both the question and the answer exist, in reality. In fact, everything you can conjure up has its place in reality. Only that which is real has existence, and only that which has existence can be known. I cannot know something that doesn't exist; for, if it doesn't exist, it is nothing. I know most people would disagree with me and say, "Santa Clause isn't real and, yet, he exists. " Yet, the question remains, where does he exist? He exists in the minds of good little boys and girls. So, in response, where does anything you have knowledge of exist? It exists in your mind.

I'm pretty sure there are a lot of things that exist apart from our knowledge of them. It sounds like you are an idealist; do you believe that reality is completely mental? Are you saying that a star or planet we don't know about cannot exist?

Can you experience anything without using your mind? Does anything exist, apart from your knowledge of it? If it does, then, tell me what it is. You can't; because, you must be conscious of it.

I believe there are a lot of things that exist apart from our knowledge of them. It sounds like you are an idealist; do you believe that reality is completely mental? Are you saying that a star or planet we don't know about cannot exist?

By definition, the term infinity, whether saying an infinitely great universe or an infinitely great set of numbers, has no end ; so, for you, or anyone else, for that matter, to make the assumption that anything is infinite is, by mere reason, a logical fallacy.

Please explain the logical argument that allows you to make the leap from "has no end" to therefore to consider anything infinite is a logical fallacy. "Has no end" is not a logical argument from which to draw your conclusion, neither is "by mere reason", please provide us with the logical argument that supports your conclusion…or acknowledge that it is nothing but an ipse dixit fallacy.

I think the real problem here is that in some people the simple abstract mathematical concept of infinity conjures up an association with theological ideas and then hardened ideological agendas come into play, people get all bunged up and emotional, and the result is a bunch of pseudo philosophical nonsense. The abstract concept of mathematical infinity is not a particularly difficult concept and it only requires a straightforward logical process of applying first order logic quantifiers, it is very useful mathematically and logically, it is definitional regarding numbers, and it just isn't about God.

How can something that, by definition, cannot be defined, define anything?

Easily, because it just isn't true that infinity, by definition, cannot be defined, we are talking about the abstract mathematical concept, and as I said, it is defined in a straightforward manner using quantifiers of first order logic. An inherent recursive function defines whole numbers as infinite, the recursive function that defines our counting system typically becomes second nature in grade school, and by the time we have finished grade school most people have accepted the concept that this recursive function can go on infinitely. it isn't rocket science.

If you have a logical argument that refutes this simple fact, I'd sure like to hear it.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
s-anthony
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8/23/2012 11:45:52 PM
Posted: 4 years ago
At 8/23/2012 1:57:51 PM, Sidewalker wrote:
I'm pretty sure there are a lot of things that exist apart from our knowledge of them. It sounds like you are an idealist; do you believe that reality is completely mental? Are you saying that a star or planet we don't know about cannot exist?

I'm not saying a star, planet, or earthworm outside of our knowledge cannot exist. Neither am I saying all that exists is mental. That which I am saying is you can only know about its existence, through your own perception of it. You cannot prove or demonstrate its existence, apart from using your brain.

Please explain the logical argument that allows you to make the leap from "has no end" to therefore to consider anything infinite is a logical fallacy. "Has no end" is not a logical argument from which to draw your conclusion, neither is "by mere reason", please provide us with the logical argument that supports your conclusion…or acknowledge that it is nothing but an ipse dixit fallacy.

Infinity as classically defined means unlimited, without bounds, without an end. If you choose to use the term in the sense, that, it has limits, then, by all means do so; but, please, drop the prefix in-, meaning without; for, to keep it is a tad bit disingenuous.

Notwithstanding, if we can proceed with the classical definition, something that is unlimited cannot be measured. If it has the quality of measurability, then, it cannot be unlimited. You cannot say something is immeasurable and, then, proceed to measure it; this is a contradiction in terms.
Sidewalker
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8/24/2012 10:40:44 AM
Posted: 4 years ago
At 8/23/2012 11:45:52 PM, s-anthony wrote:
At 8/23/2012 1:57:51 PM, Sidewalker wrote:
I'm pretty sure there are a lot of things that exist apart from our knowledge of them. It sounds like you are an idealist; do you believe that reality is completely mental? Are you saying that a star or planet we don't know about cannot exist?

I'm not saying a star, planet, or earthworm outside of our knowledge cannot exist. Neither am I saying all that exists is mental. That which I am saying is you can only know about its existence, through your own perception of it. You cannot prove or demonstrate its existence, apart from using your brain.

OK, and I concur.

Please explain the logical argument that allows you to make the leap from "has no end" to therefore to consider anything infinite is a logical fallacy. "Has no end" is not a logical argument from which to draw your conclusion, neither is "by mere reason", please provide us with the logical argument that supports your conclusion…or acknowledge that it is nothing but an ipse dixit fallacy.

Infinity as classically defined means unlimited, without bounds, without an end.

Yeah, I know, and that is how the mathematical concept is used, to represent unbounded limits, recursive processes, and endlessly repeating operations, this is what makes the concept useful and valid in mathematics.

If you choose to use the term in the sense, that, it has limits, then, by all means do so; but, please, drop the prefix in-, meaning without; for, to keep it is a tad bit disingenuous.

I don't think anybody is using it is a sense that it has limits, so there is no contradiction, and nobody is being disingenuous. Are you thinking that something can't be in a set unless it is finite? That isn't what the right side bracket means, this is a perfectly valid notation of a set (1,2,3...), and that one happens to be infinite.

Notwithstanding, if we can proceed with the classical definition, something that is unlimited cannot be measured. If it has the quality of measurability, then, it cannot be unlimited. You cannot say something is immeasurable and, then, proceed to measure it; this is a contradiction in terms.

That's a straw man too, nobody is saying it's a measurable quantity, we are saying that it's mathematically useful to be able to designate operations that result in immeasurable or unbounded results. There are plenty of infinite series and sequences, infinite sums and products, and limits approaching infinity in mathematics, the mathematical concept is therefore valid and useful. The set of integers is infinite, that doesn't mean the size of the set is measurable; it just means we can define the set by a first order logical process that recognizes it is endlessly repeating.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
s-anthony
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8/25/2012 9:43:57 AM
Posted: 4 years ago
At 8/24/2012 10:40:44 AM, Sidewalker wrote:

I think that which it all boils down to is you believe something can be infinitely large, having innumerable parts; and, I believe infinity has no parts. Let me demonstrate: firstly, you can't say something is innumerable and, then, proceed to enumerate it. You can't say something is immeasurable and, then, measure out its parts. You can't say something is beyond weight and, then, say you have weighed out a pound. In other words, you can't say the glass is empty yet part of it is full; the room is pitch black yet one corner of it is well lit. That would be like saying I am completely well yet I have a cold in me nose.

Secondly, something which is finite can't define that which is infinite. In other words, you can't say numbers go on forever; because, in order to do so, you would have to live beyond eternity, beyond the outer limits of infinity; and, again, this is a contradiction in terms.
tBoonePickens
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8/27/2012 2:12:30 PM
Posted: 4 years ago
At 8/25/2012 9:43:57 AM, s-anthony wrote:
I think that which it all boils down to is you believe something can be infinitely large, having innumerable parts; and, I believe infinity has no parts.
You can have all the belief you want regarding infinity; however, this is not akin to knowing infinity.

Let me demonstrate: firstly, you can't say something is innumerable and, then, proceed to enumerate it.
Sure you can: you can attempt to innumerate it but fail at the task.

You can't say something is immeasurable and, then, measure out its parts.
See above.

You can't say something is beyond weight and, then, say you have weighed out a pound.
See above.

In other words, you can't say the glass is empty yet part of it is full;
A glass can never be completely empty of ALL things, it can only be empty of specific things.

Secondly, something which is finite can't define that which is infinite.
And thus the infinite cannot be defined! Definitions are finite things; ergo, all knowledge is based on finite things. Thus the infinite is meaningless!

In other words, you can't say numbers go on forever; because, in order to do so, you would have to live beyond eternity, beyond the outer limits of infinity; and, again, this is a contradiction in terms.
As is your concept of infinity!
WOS
: At 10/3/2012 4:28:52 AM, Wallstreetatheist wrote:
: Without nothing existing, you couldn't have something.
CarlosMarti123
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8/28/2012 3:27:41 PM
Posted: 4 years ago
At 8/21/2012 1:17:30 PM, s-anthony wrote:
Can you measure an infinite line? If so, who decides what an inch of that line is? Can you say I traveled one mile along an infinite pathway or spent one hour of eternity? If you had an endless amount of money, could you say one tenth has been spent?

The question remains, what are you measuring against, an inch, a mile, an hour, or a tenth of what? Measurements are merely meant to quantify an object, and quantification demands a set amount. For instance, an inch is one-tweflth of a foot, and a foot is one-third of a yard, a yard is merely three feet of a mile, and a mile etc.... With infinity we would go on forever, never reaching its greatest length. In fact, it has no end. It cannot be defined, by any sort of measurement. This same idea not only applies to the line but any thing you choose to modify.

See transfinite ordinal and cardinal arithmetic.

http://blog.wolframalpha.com...
tBoonePickens
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8/28/2012 6:06:57 PM
Posted: 4 years ago
At 8/27/2012 2:15:15 PM, FREEDO wrote:
All measurements are imaginary.
As opposed to being what?
WOS
: At 10/3/2012 4:28:52 AM, Wallstreetatheist wrote:
: Without nothing existing, you couldn't have something.
s-anthony
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8/28/2012 11:13:58 PM
Posted: 4 years ago
At 8/27/2012 2:12:30 PM, tBoonePickens wrote:
Let me demonstrate: firstly, you can't say something is innumerable and, then, proceed to enumerate it.
Sure you can: you can attempt to innumerate it but fail at the task.

Infinity either has the condition of being enumerable or it doesn't. You can't say it is countable and, then, say it isn't; for, if you say infinity is innumerable and, then, enumerate it, then, you can't say it's infinity for you've said infinity is innumerable.
tBoonePickens
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8/29/2012 1:55:42 PM
Posted: 4 years ago
At 8/28/2012 11:13:58 PM, s-anthony wrote:
At 8/27/2012 2:12:30 PM, tBoonePickens wrote:
Let me demonstrate: firstly, you can't say something is innumerable and, then, proceed to enumerate it.
Sure you can: you can attempt to innumerate it but fail at the task.

Infinity either has the condition of being enumerable or it doesn't. You can't say it is countable and, then, say it isn't; for, if you say infinity is innumerable and, then, enumerate it, then, you can't say it's infinity for you've said infinity is innumerable.
Infinity defined as you claim is INDEFINITE = UNSURE = DON'T KNOW = NO KNOWLEDGE = CONTRADICTION.
WOS
: At 10/3/2012 4:28:52 AM, Wallstreetatheist wrote:
: Without nothing existing, you couldn't have something.
s-anthony
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8/29/2012 11:00:26 PM
Posted: 4 years ago
At 8/29/2012 1:55:42 PM, tBoonePickens wrote:
Infinity defined as you claim is INDEFINITE = UNSURE = DON'T KNOW = NO KNOWLEDGE = CONTRADICTION.

I agree knowing infinity is equivalent to knowing nothing; you can't know nothing; therefore, you can't know infinity. So, when we define something that is indefinite, we are not, in fact, defining that which is indefinite but, rather yet, its symbol. Human ideation is mere symbolism. Very little meaning, if any, we give to objects in our world, is exhaustive.
Sidewalker
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8/30/2012 5:10:46 AM
Posted: 4 years ago
At 8/29/2012 11:00:26 PM, s-anthony wrote:
At 8/29/2012 1:55:42 PM, tBoonePickens wrote:
Infinity defined as you claim is INDEFINITE = UNSURE = DON'T KNOW = NO KNOWLEDGE = CONTRADICTION.

I agree knowing infinity is equivalent to knowing nothing; you can't know nothing; therefore, you can't know infinity.

You are talking about infinity aren't you? You have very definite ideas about it and you are making an argument, if it is so mysterious and unknowable, then what are you talking about? Are you saying you don't know what you are talking about? Are you your own opponent in this debate?

So, when we define something that is indefinite, we are not, in fact, defining that which is indefinite but, rather yet, its symbol.

So what, defining something as indefinite is defining it. The correspondence theory of truth requires representation, and the concept of infinity is explicitly defined using the simple application of first order logic. To make an argument you need to define your terms, you are using the word infinity and presuming it's definition in your argument, it's contradictory tend that the concept you are using and applying a "logical" argument to is not defined. It's a contradiction to equate infinity to nothing and contend that it can't be known, your argument becomes self refuting and meaningless.

Human ideation is mere symbolism. Very little meaning, if any, we give to objects in our world, is exhaustive.

What do you mean "mere" symbolism, it's what we have to work with. The words you use to argue this point are symbols, the concepts you use are a matter of human ideation. We are the animal that uses symbols, it's a defining feature of human beings, the language we use, the concepts we formulate, the reason we employ, are all dependent on symbolism. The truth you are attempting to establish is a matter of correspondence to reality, correspondence is dependent on representation, and representation is a matter of using symbols.

There isn't much you are saying about infinity that you can't say about your argument, it appears to be absolutely self refuting. If you apply your argument to your argument, you prove that your argument is meaningless don't you? Doesn't your argument become equivalent to nothing also?

Unless your point is you have no point and your argument is that you have no argument, I think you need to try a different approach.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
Sidewalker
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8/30/2012 6:25:16 AM
Posted: 4 years ago
At 8/25/2012 9:43:57 AM, s-anthony wrote:
At 8/24/2012 10:40:44 AM, Sidewalker wrote:

I think that which it all boils down to is you believe something can be infinitely large, having innumerable parts; and, I believe infinity has no parts.

I think what it all boils down to is you and I are using the same definition of infinity, and it's the one we learned in grade school, the one defined by the simple application of first order logic that we both understood in grade school. I believe we are having a discussion about it, and you believe you can convince me that the subject of our discussion doesn't exist. You are using the commonly agreed upon definition of the term to argue that that there is no definition, and you have defined it in the same way I have, as endlessly repeating, in order to then argue that it can't be endlessly repeating. I'm pretty sure you are contradicting your own contradictions, or something like that, I am inclined to try to follow your logic to a conclusion that demonstrates how your reasoning leads to an endlessly repeating self referential loop, but I'm afraid it will make my head explode and I'm thinking I might need it later.

Let me demonstrate: firstly, you can't say something is innumerable and, then, proceed to enumerate it.

No, you can't, and you can't say something is defined as endlessly repeating and then proceed to argue that it isn't defined because it is endlessly repeating.

You can't say something is immeasurable and, then, measure out its parts. You can't say something is beyond weight and, then, say you have weighed out a pound. In other words, you can't say the glass is empty yet part of it is full; the room is pitch black yet one corner of it is well lit. That would be like saying I am completely well yet I have a cold in me nose.

Those are all nice analogies about something, but they just aren't about the subject we happen to be discussing.

Secondly, something which is finite can't define that which is infinite.

I/m pretty sure you and I are finite, and we both defined infinity, in fact, it was the logical starting point from which we both rationally proceeded to make an argument, and now you are attempting to argue that the concept can't be defined? I don't think that works.

In other words, you can't say numbers go on forever; because, in order to do so, you would have to live beyond eternity, beyond the outer limits of infinity; and, again, this is a contradiction in terms.

I'll bet you said numbers go on forever in grade school, I know you thought it, and I know you still think it, you've admitted that, and I hate to be the one to break it to you, but neither one of us is are going to live beyond eternity.

That was sarcasm of course, I know you know that, and given that you know that, it's your argument that is a contradiction in terms. By the very reasoning of your own argument, you don't have an argument, and that's about as contradictory as you can get.

I didn't even have to show up to win this debate, you are refuting your argument for me, and you are doing a great job of it.

Thank you.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
s-anthony
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8/30/2012 9:52:55 AM
Posted: 4 years ago
At 8/30/2012 5:10:46 AM, Sidewalker wrote:
You are talking about infinity aren't you? You have very definite ideas about it and you are making an argument, if it is so mysterious and unknowable, then what are you talking about? Are you saying you don't know what you are talking about? Are you your own opponent in this debate?

Talking about an accepted definition, or representation, of something is in no way exhaustive. Of course, we define infinity, just as we define the night sky when we look up at night. Our vision is limited and, therefore, limits our empirical knowledge of something. Yet, would anyone assume he, or she, has an unlimited view of the Universe?

However, defining the night sky and defining infinity are two separate matters. As to where one is said to be teeming with substance, the other, by definition, is endless. In saying, you cannot define infinity, I'm not in anyway saying infinity is meaningless; yet, if given the classical definition, you cannot break it up into parts. In other words, you can't say something is innumerable and, then, enumerate it.

So what, defining something as indefinite is defining it. The correspondence theory of truth requires representation, and the concept of infinity is explicitly defined using the simple application of first order logic. To make an argument you need to define your terms, you are using the word infinity and presuming it's definition in your argument, it's contradictory tend that the concept you are using and applying a "logical" argument to is not defined. It's a contradiction to equate infinity to nothing and contend that it can't be known, your argument becomes self refuting and meaningless.

No. I'm not saying nothing can't be known, but, rather yet, all that can be known of nothing is nothing; for, that's what it is, nothing.